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Math Help - Indeterminant limit involving an integral.

  1. #1
    Member sbhatnagar's Avatar
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    Question integral limit question: please help me

    The value of is :
    (a) 0
    (b)1/12
    (c)1/24
    (d)1/64
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  2. #2
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    Re: integral limit question: please help me

    First, expand to series t(1+t)/(4+t^4) = t/4 - (t^3)/8 +O(t^4)
    Second, integration from t=0 to x leads to I= (x^3)/12 - (x^4)/32 +O(x^5)
    Then, I/x^3 = 1/12 + x/32 +O(x) which limit for x -> 0 is 1/12
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  3. #3
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    Re: integral limit question: please help me

    Quote Originally Posted by sbhatnagar View Post
    The value of is :
    (a) 0
    (b)1/12
    (c)1/24
    (d)1/64
    Use l'Hospital's Rule:

    The derivative of the numerator is (using the Fundamental Theorem of Calculs) \frac{x \ln(1 + x)}{x^4 + 4} and the derivative of the denominator is 3x^2. Therefore ....
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  4. #4
    Member sbhatnagar's Avatar
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    Exclamation Re: integral limit question: please help me

    Thank You! I got it->







    Last edited by sbhatnagar; September 18th 2011 at 02:02 AM.
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